Question 1

Two-third of the number of employees of a companyare males andthe rest are females. If $$\frac{3}{8}$$ of the male employees and $$\frac{2}{5}$$ of the female employees are temporary employees and the total number of permanent employees is 740. then $$\frac{7}{15}$$ of the total number of employees exceeds the number of temporary female employees by:

Solution

let the total employees be x.
Male employees = $$\frac{2x}{3}$$
Female employees = x - $$\frac{2x}{3}$$ = $$\frac{x}{3}$$
Permanent male employees = 1 - $$\frac{3}{8}$$ = $$\frac{5}{8}$$ of the male employee = $$\frac{2x}{3} \times \frac{5}{8}$$ = $$\frac{5x}{12}$$
Permanent female employees = 1 - $$\frac{2}{5}$$ = $$\frac{3}{5}$$ of the male employee = $$\frac{x}{3} \times \frac{3}{5}$$ = $$\frac{x}{5}$$
Total number of permanent employees = 740
$$\frac{5x}{12}$$ + $$\frac{x}{5}$$ = 740
$$\frac{37x}{60}$$ = 740
x = 740 $$\times \frac{60}{37} = 1200$$
$$\frac{7}{15}$$ of the total number of employees = 1200 $$\times \frac{7}{15}$$ = 560
Number of temporary female employees = $$\frac{x}{3} \times \frac{2}{5}$$ = $$\frac{2x}{15}$$
= $$\frac{2 \times 1200}{15}$$ = 160
$$\frac{7}{15}$$ of the total number of employees exceeds the number of temporary female employees by = 560 - 160 = 400


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